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Re: [ontolog-forum] FW: Lattice of theories

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 16 Jan 2009 12:37:30 -0500
Message-id: <4970C5DA.8050307@xxxxxxxxxxx>
Len,    (01)

As I said, they are "often" called axioms.    (02)

JFS>> All the ontologies that have been proposed so far have been
 >> collections of statements (often called axioms) in some
 >> version of logic.    (03)

LY> I think that you are talking about different ontologies here.
 > Using Semantic Web terminology the set of axioms is called "T-Box"
 > (if I not mistaken "T" refers to taxonomy or terminology or both)
 > The is also so called A-Box http://en.wikipedia.org/wiki/ABox    (04)

The terms T-box (Terminology statements) and A-Box (Assertion
statements) were introduced with KL-ONE, an early definition logic.
(But if you consider Aristotle's syllogisms the most widely used
definition logic of all time, then everything else is late.)  Since
many of the people who developed OWL came from the DL community,
they tended to use that terminology.    (05)

LY> It seems that Sean is calling T-Box a "data model" and his concern
 > is that the lattice of T-Boxes is not useful for some reasoning with
 > A-Boxes.    (06)

The term 'data model' comes from the database community, which is
nearly disjoint from the DL-community.  That is one of my primary
complaints about the Semantic Web:  they did not integrate both
communities.  That is a serious deficiency, since the DB community
is far and away the largest consumer and developer of logic-based
technology for commercial applications.    (07)

In the DB community, the statements in the T-box correspond to
the database schema and the constraints on permissible updates.    (08)

JFS>> If by grounding, [Sean] means some part of the world for
 >> which some set of statements (or axioms) are true, then two
 >> identical sets of statements would be true of exactly the
 >> same parts of the world.  Therefore, identical axioms would
 >> have identical grounding.    (09)

LY> If we accept T-Box/A-box distinction, the the statement above
 > is not necessarily true.    (010)

That statement is true for all versions of logic.  Therefore, it is
true for description logics, database logics, and the Semantic Web.
It is also true for the larger, more general logics used in large
systems such as SUMO (the KIF language) and Cyc (the CycL language).
All of them are versions of logic, but they use different terminology.    (011)

Bottom line:  For the Foundation Ontology, we should use the more
general terminology of logic instead of the specialized terms used
for one special case after another.    (012)

John Sowa.    (013)

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